To assess the energy of radiation and its effect on radiation receivers, which include photoelectric devices, thermal and photochemical receivers, as well as the eye, energy and light quantities are used.
Energy quantities are characteristics optical radiation, relating to the entire optical range.
Eye for a long time was the only receiver of optical radiation. Therefore, historically it has happened that for high-quality and quantification In the visible part of the radiation, light (photometric) quantities are used that are proportional to the corresponding energy quantities.
The concept of radiation flux relating to the entire optical range was given above. The quantity that in the system of light quantities corresponds to the radiation flux,
is the luminous flux Ф, i.e. the radiation power estimated by a standard photometric observer.
Let's consider light quantities and their units, and then find the connection between these quantities and energy ones.
To evaluate two sources visible radiation their luminescence in the direction of the same surface is compared. If the glow of one source is taken as unity, then by comparing the glow of the second source with the first we obtain a value called luminous intensity.
IN International system SI units for the unit of luminous intensity is the candela, the definition of which was approved by the XVI General Conference (1979).
Candela is the luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of Hz, energetic force the light of which in this direction is
Luminous intensity, or angular density luminous flux,
where is the luminous flux in a certain direction inside the solid angle
A solid angle is a limited arbitrary conical surface part of the space. If we describe a sphere from the top of this surface as from the center, then the area of the sphere section cut off by the conical surface (Fig. 85) will be proportional to the square of the radius of the sphere:
The proportionality coefficient is the value of the solid angle.
The unit of solid angle is the steradian, which is equal to the solid angle with its vertex at the center of the sphere, cutting out the area on the surface of the sphere, equal to the area square with side equal to the radius spheres. A complete sphere forms a solid angle
Rice. 85. Solid angle
Rice. 86. Radiation in solid angle
If the radiation source is at the vertex of the straight line circular cone, then the solid angle identified in space is limited by the internal cavity of this conical surface. Knowing the value of the plane angle between the axis and the generatrix of the conical surface, we can determine the corresponding solid angle.
Let us select in the solid angle an infinitesimal angle that cuts out an infinitely narrow annular section on the sphere (Fig. 86). This case refers to the most common axisymmetric luminous intensity distribution.
The area of the annular section is where the distance from the axis of the cone to the narrow ring width
According to Fig. where is the radius of the sphere.
Therefore where
Solid angle corresponding to a plane angle
For a hemisphere, the solid angle for a sphere is -
From formula (160) it follows that the luminous flux
If the intensity of light does not change when moving from one direction to another, then
Indeed, if a light source with luminous intensity is placed at the vertex of a solid angle, then the same luminous flux arrives at any areas limited by a conical surface that distinguishes this solid angle in space. Let us take the indicated areas in the form of sections of concentric spheres with the center at the vertex of the solid angle . Then, as experience shows, the degree of illumination of these areas is inversely proportional to the squares of the radii of these spheres and directly proportional to the size of the areas.
Thus, the following equality holds: i.e., formula (165).
The given justification for formula (165) is valid only in the case when the distance between the light source and the illuminated area is sufficiently large compared to the size of the source and when the medium between the source and the illuminated area does not absorb or scatter light energy.
The unit of luminous flux is the lumen (lm), which is the flux within a solid angle when the luminous intensity of a source located at the vertex of the solid angle is equal to
The illumination of the area normal to the incident rays is determined by the ratio called illuminance E:
Formula (166), as well as formula (165), takes place under the condition that the light intensity I does not change when moving from one direction to another within a given solid angle. IN otherwise this formula will be valid only for an infinitesimal area
If the incident rays form angles with the normal to the illuminated area, then formulas (166) and (167) will change, since the illuminated area will increase. As a result we get:
When the site is illuminated by several sources, its illumination
where the number of radiation sources, i.e. the total illumination is equal to the sum of the illumination received by the site from each source.
The unit of illumination is taken to be the illumination of the site when a luminous flux falls on it (the site is normal to the incident rays). This unit is called luxury
If the dimensions of the radiation source cannot be neglected, then to solve a number of problems it is necessary to know the distribution of the light flux of this source over its surface. The ratio of the luminous flux emanating from a surface element to the area of this element is called luminosity and is measured in lumens per square meter Luminosity also characterizes the distribution of reflected light flux.
Thus, the luminosity
where is the surface area of the source.
The ratio of the intensity of light in a given direction to the area of projection of the luminous surface onto a plane perpendicular to this direction is called brightness.
Therefore, the brightness
where is the angle between the normal to the site and the direction of the light intensity
Substituting the value [see. formula (160)), we obtain that the brightness
From formula (173) it follows that the brightness is the second derivative of the flux with respect to the solid angle to the area.
The unit of brightness is candela per square meter
Surface density The light energy of the incident radiation is called exposure:
IN general case illumination included in formula (174) can change over time
The exposition has a large practical significance, for example in photography and is measured in lux seconds
Formulas (160)-(174) are used to calculate both light and energy quantities, firstly, for monochromatic radiation, i.e. radiation with a certain wavelength, and secondly, in the absence of taking into account the spectral distribution of radiation, which, usually occurs in visual optical instruments.
The spectral composition of radiation - the distribution of radiation power over wavelengths has great importance for calculating energy quantities when using selective radiation receivers. For these calculations, the concept of spectral density radiation flux [see formulas (157)-(159)].
In a limited range of wavelengths, we respectively have:
The energy quantities determined by the formulas also apply to the visible part of the spectrum.
Basic photometric and energy quantities, their defining formulas and SI units are given in Table. 5.
Luminous flux - the power of light energy, an effective value measured in lumens:
Ф = (JQ/dt. (1.6)
The unit of luminous flux is lumen (lm); 1 lm corresponds to the luminous flux emitted in a unit solid angle by a point isotropic source with a luminous intensity of 1 candela (the definition of capdela will be lower).
Monochromatic luminous flux
F(A. dk) = Kt. m Fe,(L, dk)Vx = 683Fe,(A, dk)Vx.
Luminous flux of complex radiation: with a line specter
Ф=683£Ф,(Л„ dk)VXh
with continuous spectrum
where n is the number of lines in the spectrum; F<>D, (A.) is a function of the spectral radiation flux density.
Sshsh study (luminous energy intensity) 1e(x^ - spatial radiation flux density, numerically equal to the ratio radiation flux c1Fe to the solid angle t/£2, within which the flux spreads and is uniformly distributed:
>ea v=d The radiation strength determines the spatial density of radiation from a point source located at the apex of the solid angle (Fig. 1.3). The direction 1ef is taken to be the axis of the solid angle dLl. oriented by angles a and P in the longitudinal and transverse planes. The unit of radiation power W/sr has no name. The spatial distribution of the radiation flux of a point source is uniquely determined by its photometric body - a part of space limited by the surface drawn through the ends of the radius vectors of the radiation force. A section of a photometric gel by a plane passing through the origin and a point source determines the luminous intensity curve (LIC) of the source for a given section plane. If the photometric body has an axis of symmetry, the radiation source is characterized by the KSS in the longitudinal plane (Fig. 1.4). Radiation flux of a point circularly symmetrical radiation source F? = jle(a)dLi = 2л J le(a) sin ada, where Dj is the zonal solid angle within which the source radiation propagates; determined in the longitudinal plane by the angles “| and a„. Luminous intensity of a point source - spatial density of luminous flux laf,=dФ/dQ. (1.8) Candela (cd) is a unit of luminous intensity (one of the basic SI units). The candela is equal to the intensity of light emitted in a perpendicular direction from an area of 1/600000 m2 of a black body at the solidification temperature of platinum T = 2045 K and a pressure of 101325 Pa. The luminous flux of an IC is determined by the KSS if the photometric body has an axis of symmetry. If KSS / (a) is given by a graph or table, the calculation of the luminous flux of the source is determined by the expression F=£/shdts-,+i, where /w is the srslnss value of the luminous intensity in the zonal solid angle; Dy, (+| = 2n(cos a, - cos a,_|) (see Table 1.1). Energy luminosity (emissivity) is the ratio of the radiation flux emanating from the small surface area under consideration to the area of the area: M e = (1Fe / dA; Mesh>=Fe/A, (1.9) where d$>e and Ф(. are the radiation fluxes emitted by the surface area dA or surface A. Unit energetic luminosity(W/m2) - flux and heaving. emitted from 1 m2 of surface; this unit has no name. Luminosity is the ratio of the luminous flux emanating from the small surface area under consideration to the area of this area: M =
where еФ and Ф are the luminous fluxes emitted by surface area dA or surface A. Luminosity is measured in lm/m2 - this is the luminous flux emitted from 1 m2. Energy illumination (irradiance) - the density of the radiant flux of the irradiated surface E = (1Fe/c1A; Eecr = Fe/A, (1.11) where Ee, Eсr are, respectively, the irradiance of the surface area dA and the average irradiance of the surface A. Per unit of irradiance. Vg/m2. they accept such irradiance at which 1 W of radiant flux falls and is evenly distributed over a surface of 1 m2; this unit has no name. Illumination - the density of luminous flux on the illuminated surface dF.=d<>/dA Esr - F/L, (1.12) where dE and Еср are the illumination of the surface area dA and the average illumination of the surface A. The unit of illumination is lux (lx). Illumination of 1 lux has a surface on which 1 m2 of light falls and a luminous flux of 1 lm is distributed evenly over it. The energetic brightness of a body or a section of its surface in direction a is the ratio of the radiation force in direction a to the projection of the radiating surface onto a plane perpendicular to this direction (Fig. 1.5): ~ dIshkh / (dA cos ss), ~ ^ey. ^" (1-13) where Leu and Lcr are the energy brightnesses of the surface area dA and surface A in the direction a, the projections of which onto a plane perpendicular to this direction are respectively equal to dAcosa and a; dleu and 1еа are respectively the radiation forces emitted by dA and A in the direction of a. The unit of energy brightness is taken to be the energy brightness of a flat surface B 1 M“. having a radiation force of 1 Vg/sr in the perpendicular direction. This unit (W/srm2) has no name. The brightness in direction a of a body or part of its surface is equal to the ratio of the light intensity in this direction to the projection of the surface: La = dIa/(dAcosa); /.acr = /a/a, (1.14) where /u and Lacr are the brightness of the surface area dA and surface A in the direction a. the projections of which onto a plane perpendicular to this direction are respectively equal to dA cos a and a; dla. 1a - respectively, the luminous intensities emitted by the surfaces dA and A in the direction a. The unit of brightness measurement (cd/m2) is the brightness of a flat surface that emits a luminous intensity of 1 cd from an area of 1 m in a perpendicular direction. Equivalent brightness. Under conditions of twilight vision, the relative spectral light efficiency of the organ of vision depends on the level of adaptation Y(X, /.) and occupies an intermediate position between K(A) and Y"(X), shown in Fig. 1.2. Under these conditions, their values are different spectral composition, identical in brightness for daylight vision, will be of different brightness for the eye (Purkins effect). For example, blue will be brighter than red. In the field of twilight vision, the concept of equivalent brightness is used. You can select radiation of a certain spectral composition, for which the brightness at all levels is assumed to be proportional to the radiation power. A. A. Gershun |1] proposed as such an interpretation. called reference, use black body radiation at the solidification temperature of platinum. A radiation of a different spectral composition, equal in brightness to the reference one, will have the same equivalent brightness, although the standard brightness of the radiation will be different. Equivalent brightness makes it possible to compare different radiations according to their luminous effect, even under conditions of uncertainty in the relative spectral sensitivity function. Flux (power) of radiation (F) yavl. the main quantity in the energy measurement system. The power (or flux) of radiation is taken to be the energy transferred per unit time. The value of F is expressed in watts (W). Electromagnetic wave range hesitation, noun in nature, it is quite wide and extends from fractions of an angstrom to a kilometer. Gamma rays _____________________________________ less than 0.0001 X-rays______________________________ 0.01-0.0001 Ultraviolet rays______________________________ 0.38-0.01 Visible light_____________________________________________ 0.78-0.38 Infrared rays ________________________________1000-0.78 Radio waves__________________________________________ more than 1000 The optical region of the spectrum includes only a part of electromagnetic radiation with a wavelength interval from λmin = 0.01 μm to λmax = 1000 μm. Such radiation is created as a result of electromagnetic excitation of atoms, vibrational and rotational motion of molecules. The optical spectrum can be divided into three main regions: ultraviolet, visible, and infrared. Ultraviolet radiation produces the most powerful photons and has a strong photochemical effect. The emission of visible light, despite a rather narrow interval, allows us to see all the diversity of the world around us. So, the human eye practically does not perceive radiation with extreme wavelength ranges (they have a weak effect on the eye); in practice, visible light is considered to be radiation with a wavelength range of 400-700 nm. This radiation has significant photophysical and photochemical effects, but less than ultraviolet radiation. Photons of infrared radiation have the minimum energy from the entire optical region of the spectrum. This radiation is characterized by thermal action and, to a much lesser extent, photophysical and photochemical. action. 2. The concept of a radiation receiver
. Receiver reactions. Classification of radiation successors. Linear and nonlinear receivers. Spectral sensitivity of the radiation receiver. bodies in which such transformations occur under the influence of optical radiation have received the general name in lighting engineering "radiation receivers" Conventionally, radiation receivers are divided into: 1. The natural receiver of radiation is the human eye. 2. Photosensitive materials used for optical recording of images. 3. Receivers are also photosensitive elements of measuring instruments (densitometers, colorimeters) Optical radiation has high energy and therefore affects many substances and physical bodies. As a result of the absorption of light in media and bodies, a number of phenomena arise (Fig. 2.1, sir 48) A body that has absorbed radiation begins to radiate itself. In this case, the secondary radiation may have a different spectral range compared to the absorbed one. For example, when illuminated with ultraviolet light, the body emits visible light. The energy of absorbed radiation is converted into electrical energy, as in the case of the photoelectric effect, or produces a change in the electrical properties of the material, which occurs in photoconductors. Such transformations are called photophysical. Another type of photophysical transformation is the transition of radiation energy into thermal energy. This phenomenon has found application in thermocouples used to measure radiation power. Radiation energy is converted into chemical energy. A photochemical transformation of the substance that has absorbed light takes place. This transformation occurs in most photosensitive materials. Bodies in which such transformations occur under the influence of optical radiation have received the general name in lighting engineering. "radiation receivers" Linear nonlinear receivers??????????????????
Spectral sensitivity of the radiation receiver. Under the influence of optical radiation, a photochemical and photophysical transformation occurs in the receiver, changing the properties of the receiver in a given way. This change is called the useful response of the receiver. However, not all the energy of the incident radiation is spent on a useful reaction. Some of the energy of the receivers is not absorbed and therefore cannot cause a reaction. The absorbed energy is also not completely converted usefully. For example, in addition to the photochemical transformation, heating of the receiver can occur. The practically used part of the energy is called. useful, and the practically used part of the radiation power (radiation flux F) is the effective flux Ref. The ratio of the effective flux Ref to the radiation flux incident on the receiver called sensitivity of the receiver. For most receivers, spectral sensitivity depends on wavelength. Sλ= сРλ eff/Фλ and Рλ eff=КФλSλ The quantities are called Фλ and Рλ, respectively, monochromatic radiation flux and monochromatic effective flux, and Sλ is called monochromatic spectral sensitivity. Knowing the power distribution over the spectrum Ф(λ) for radiation incident on the receiver and the spectral sensitivity of the receiver S(λ), we can calculate the effective flux using the formula – Ref=К ∫ Ф(λ)S(λ)dλ The measurement refers to a range of ∆λ, limited either by the spectral sensitivity of the receiver or by the spectral range of the measurement. 3.Features of the eye as a receiver. Light flow. Its connection with the radiation flux. Visibility curve. The difference in light and energy fluxes is in the range of 400-700 nm.
The visual apparatus consists of a radiation receiver (eyes), optic nerves and visual areas of the brain. In these zones, signals generated in the eyes and transmitted through the optic nerves are analyzed and converted into visual images. The radiation receiver consists of two eyeballs, each of which, with the help of six external muscles, can easily rotate in the orbit both in the horizontal and vertical plane. When viewing an object, the eyes move spasmodically, alternately fixating on different points of the object. This movement is vector in nature, i.e. the direction of each jump is determined by the object in question. The speed of the jump is very high, and the fixation points where the eye stops for 0.2-0.5 s are located mainly at the boundaries of parts where there are differences in brightness. During “stops,” the eye is not at rest, but makes rapid micro-movements relative to the point of fixation. Despite these microsaccades, at the fixation points, the observed area of the object is focused on the central fovea of the photosensitive retina of the eyes. Fig.2.4 (Horizontal section of the eye) p.56 Light flow(F) Luminous flux is, in general, understood as the radiation power assessed by its effect on the human eye. The unit of measurement for luminous flux is lumen (lm). The action of the light flux on the eye causes it to react in a certain way. Depending on the level of action of the light flux, one or another type of light-sensitive receptors of the eye, called rods or cones, works. In low light conditions (for example, in the light of the moon), the eye sees surrounding objects using rods. At high light levels, the daytime vision apparatus, for which the cones are responsible, begins to work. In addition, cones, based on their light-sensitive substance, are divided into three groups with different sensitivity in different regions of the spectrum. Therefore, unlike rods, they react not only to the light flux, but also to its spectral composition. In this regard, we can say that the effect of light is two-dimensional. A quantitative characteristic of the eye's reaction associated with the level of illumination, called. light. A qualitative characteristic associated with different levels of reaction of the three groups of cones is called chromaticity. An important characteristic is the distribution curve of the relative spectral sensitivity of the eye (relative spectral luminous efficiency) in daylight νλ =f(λ) Fig. 1.3 p.9 In practice, it has been established that in daylight conditions the human eye has maximum sensitivity to radiation with Lambda = 555 nm (V555 = 1). Moreover, each unit of luminous flux from F555 has radiation power Ф555 = 0.00146 W. The ratio of the luminous flux F555 to Ф555 is called spectral luminous efficiency. Or for any wavelength of radiation in the visible range K=const: К=1/V(λ) *F λ /Ф λ =680. (1) Using formula (1) it is possible to establish a connection between the luminous flux and the radiation flux. Fλ = 680 *Vλ * Фλ For integral radiation F= 680 ∫ Vλ Фλ dλ 4. Photoactinic flow. Understanding efficient flow. Monochromatic and integral flows. Actinism
.
In lighting and reproduction technology, two types of effective fluxes are used: light F and photoactinic A. The luminous flux is related to the power (radiation flux F) by the following expression: F=680 ∫ Ф(λ) V(λ) dλ 400 nm If a luminous flux falls on any surface, its surface density is called illuminance. Illumination E is related to luminous flux by the formula Where Q is the area in m. The unit of illumination is lux (cl) For photosensitive materials and photodetectors of measuring instruments use photoactinic fluxA.
This is the effective flow defined by If the spectral range in which the measurement is made is limited by the wavelengths λ1 and λ2, then the expression for photoactinic flux will take the form A = ∫ Ф(λ) * S (λ) dλ λ 1 m/J, then this will affect the dimension of the photoactinic flux Surface density of photoactinic flux on an illuminated surface called actinic radiationa,
a=
dA/
dQ If the surface of the receiver is uniformly illuminated, then a = A/Q. For monochromatic radiation. Fλ = 680 *Vλ * Фλ For integral radiation F= 680 ∫ Vλ Фλ dλ Actinism- analogue of illumination. Its unit of measurement depends on the dimension A If A – W, then a-W/m Fig.2.2 page 52 The greater the actinicity of the radiation, the more efficiently the radiation energy is used and the more, all other things being equal, the response of the receiver will be useful. To achieve maximum actinicity, it is desirable that the maximum spectral sensitivity of the receiver and the maximum radiation power fall in the same spectral zones. This consideration guides the selection of a light source for obtaining images on a specific type of photosensitive materials. For example, the copying process. The copy layers used to make printing plates are sensitive to ultraviolet and blue-violet radiation. They do not react to radiation from other zones of the visible spectrum. Therefore, to carry out the copying process, they use Metal halide lamps, rich in ultraviolet and blue light. FIGURE 2.3. Page 53 manual 5. Color temperature. Luminosity curves of an absolute black body at different temperatures. The concept of a normalized curve. Definition of the term “color temperature”. The direction of change in the color of radiation with a change in color temperature. Color temperature means the temperature in Kelvin of a completely black body at which the radiation has the same color as the one being considered. For incandescent lamps with a tungsten filament, the spectral distribution of radiation is proportional to the spectral distribution of black body radiation in the wavelength range 360-1000 nm. To calculate the spectral composition of the radiation of an absolutely black body at a given absolute temperature of its heating, you can use Planck’s formula: e -5 s 2 / λ t Rλ =С1 λ (е -1) Where Rλ is the spectral energy luminosity, C1 and C2 are constants, e is the base of natural logarithms, T is the absolute temperature, K Experimentally, the color temperature is determined by the value of the blue-red ratio of actinicities. Actinity-illuminance effective in relation to the photodetector: Аλ = Фλ Sλ / Q = Eλ Sλ If a lux meter is used as a photodetector, then the actinicity is the illumination determined by shielding the photocell with blue and red light filters. Technically, the measurement is carried out as follows. The photocell of the luxmeter is alternately screened with specially selected blue and red light filters. Light filters must be zonal and have the same multiplicity in the transmission zone. The lux meter's galvanometer determines the illumination from the measured source for each of the filters. Calculate the blue-red ratio using the formula K = Ac / Ak = Es / Ek SCHEDULE page 6 lab slave Фλ. To do this, the values of spectral energy luminosity are calculated using Planck's formula. Next, the resulting function is normalized. Normalization consists of a proportional decrease or increase in all values in such a way so that the function passes through the point with coordinates λ = 560 nm, log R560 = 2.0 or λ = 560 nm, R560 rel = 100 In this case, it is considered that each value refers to the spectral interval ∆λ corresponding to the calculation step. ∆λ=10 nm, luminosity 100 W*m corresponds to a wavelength of 560 nm in the wavelength range 555-565 nm. Fig 1.2 Page 7 lab slave Using the spectral dependence function Rλ = f λ, you can find the functions E λ = Фλ = f λ To do this, you need to use the formulas E - illumination, R - luminosity, F - energy flow, Q - area Depending on the ratio of the dimensions of the emitter and its distance to the field point under study, radiation sources can be divided into 2 groups: 1) point sources of radiation 2) a source of finite dimensions (linear source) A radiation source whose dimensions are significantly less than the distance to the point under study is called a point source. In practice, a point source is taken to be one whose maximum size is at least 10 times less than the distance to the radiation receiver. For such radiation sources, the inverse square law of distance is observed. E=I/r 2 cosine alpha, where alpha=angle between the light ray and the perpendicular to the surface C. If from the point at which a point source of radiation is located, vectors of unit radiation strength are plotted in different directions of space and a surface is drawn through their ends, then a PHOTOMETRIC BODY of the radiation force of the source is obtained. Such a body completely characterizes the distribution of the radiation flux of a given source in the space surrounding it. 8. Transformation of radiation by optical media. Characteristics of radiation conversion: light coefficients, multiplicities, optical densities, connections between them. Light filters Definition of the term. Spectral curve as a universal characteristic of a light filter. When a radiation flux F0 hits a real body (optical medium), part of it F(ro) is reflected by the surface, part of F(alpha) is absorbed by the body, and part of F(tau) passes through it. The ability of a body (optical medium) to undergo such a transformation is characterized by the reflection coefficient rho=Fro/F0, the coefficient tau=Ftau/F0. If the coefficients are determined by converting light fluxes (F, lm), then they are called light (photometric) Rosv = Fo/Fo; Alphasw=Falpha/Fo;tausw=Ftau/Fo For optical and light coefficients, the statement is true that their sum is equal to 1.0 (po+alpha+tau=1) There are two more types of coefficients - monochromatic and zonal. The first evaluate the effect of the optical medium on monochromatic radiation with a lambda wavelength. Zonal coefficients evaluate the conversion of radiation occupying from the spectrum zones (blue with delta lambda = 400-500 nm, green with delta lambda = 500-600 nm and red with delta lambda = 600-700 nm) 9. Bouguer-Lambert-Beer law. Quantities bound by law. Additivity of optical densities, as the main conclusion from the Bouguer-Lambert-Beer law. Light scattering indicatrices, turbidity of media. Types of light scattering. F 0 /F t =10 kl, k-absorption index. Beer established that the absorption index also depends on the concentration of the light-absorbing substance c, k = Xc, x is the molar absorption index, expressed as the reciprocal of the thickness of the layer that attenuates light 10 times when the concentration of the light-absorbing substance in it is 1 mol/l. The final equation expressing the Bouguer-Lambert-Beer law looks like this: Ф0/Фт=10 to the power Хс1 The luminous flux transmitted by the layer is related to the incident flux exponentially through the molar absorption coefficient, the thickness of the layer and the concentration of the light-absorbing substance. The physical meaning of the concept of optical density follows from the law considered. Having integrated the expression Ф0/Фт=10 to the power of Хс1 We get D=X*s*l, those. The optical density of the medium depends on its nature and is proportional to its thickness and the concentration of the light-absorbing substance. Since the Bouguer-Lambert-Beer law characterizes the fraction of absorbed light through the fraction of transmitted light, it does not take into account reflected and scattered light. In addition, the resulting relationship expressing the Bouguer-Lambert-Beer law is valid only for homogeneous media and does not take into account the loss of light reflection from the surface of bodies. Deviation from the law leads to non-additivity of optical media. Photometry is the branch of optics that deals with the measurement of light fluxes and quantities associated with such fluxes. The following quantities are used in photometry: 1) energy
– characterize the energy parameters of optical radiation regardless of its effect on radiation receivers; 2) light
– characterize the physiological effect of light and are assessed by the effect on the eye (based on the so-called average sensitivity of the eye) or other radiation receivers. 1. Energy quantities. Radiation flux
Φ e – value equal to the energy ratio W radiation by time t, during which the radiation occurred: The unit of radiation flux is watt (W). Energetic luminosity (emissivity)
R e– value equal to the ratio of the radiation flux Φ e emitted by the surface to the area S cross section through which this flow passes: those. represents the surface radiation flux density. The unit of energetic luminosity is watt per square meter (W/m2). Radiation intensity: where Δ S– a small surface perpendicular to the direction of radiation propagation through which the flux ΔΦ e is transferred. The unit of measurement for radiation intensity is the same as for energetic luminosity – W/m2. To determine subsequent quantities, you will need to use one geometric concept - solid angle
, which is a measure of the opening of some conical surface. As is known, the measure of a plane angle is the ratio of the arc of a circle l to the radius of this circle r, i.e. (Fig. 3.1 a). Similarly, the solid angle Ω is defined (Fig. 3.1 b) as the ratio of the surface of the spherical segment S to the square of the radius of the sphere: The unit of measurement for solid angle is steradian
(ср) is a solid angle, the vertex of which is located in the center of the sphere, and which cuts out an area on the surface of the sphere equal to the square of the radius: Ω = 1 ср, if . It is easy to verify that the total solid angle around a point is equal to 4π steradians - to do this, you need to divide the surface of the sphere by the square of its radius. Energy intensity of light (radiation power
) Ie determined using concepts about a point light source
– a source whose size compared to the distance to the observation site can be neglected. The energetic intensity of light is a value equal to the ratio of the source radiation flux to the solid angle Ω within which this radiation propagates: The unit of luminous energy is watt per steradian (W/sr). Energy brightness (radiance)
V e– a value equal to the ratio of the energy intensity of light ΔI e element of the radiating surface to the area ΔS projection of this element onto a plane perpendicular to the direction of observation: The unit of radiance is watt per steradian meter squared (W/(sr m2)). Energy illumination (irradiance)
Her characterizes the amount of radiation flux incident on a unit of illuminated surface. The irradiance unit is the same as the luminosity unit (W/m2). 2. Light quantities. In optical measurements, various radiation detectors are used (for example, the eye, photocells, photomultipliers), which do not have the same sensitivity to the energy of different wavelengths, thus being selective (selective)
. Each light receiver is characterized by its sensitivity curve to light of different wavelengths. Therefore, light measurements, being subjective, differ from objective, energy ones, and for them light units,
used for visible light only. Basic light unit
in SI is the unit of luminous intensity - candela
(cd), which is defined as the luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540·10 12 Hz, the luminous energy intensity of which in this direction is 1/683 W/sr. The definition of light units is similar to energy units. Light flow
Φ light is defined as the power of optical radiation based on the light sensation it causes (about its effect on a selective light receiver with a given spectral sensitivity). Luminous flux unit – lumen
(lm): 1 lm – luminous flux emitted by a point source with a luminous intensity of 1 cd inside a solid angle of 1 sr (with uniformity of the radiation field inside the solid angle) (1 lm = 1 cd sr). The power of light I St. is related to the luminous flux by the relation Where dΦ St– luminous flux emitted by a source within a solid angle dΩ. If I St. does not depend on direction, the light source is called isotropic.
For an isotropic source Energy flow .
Φ e, measured in watts, and luminous flux Φ St., measured in lumens, are related by the relationship: Where Luminosity
R St is determined by the relation The unit of luminosity is lumen per square meter (lm/m2). Brightness
In φ luminous surface area S in a certain direction forming an angle φ with the normal to the surface, there is a value equal to the ratio of the intensity of light in a given direction to the area of the projection of the luminous surface onto a plane perpendicular to this direction: Sources whose brightness is the same in all directions are called Lambertian
(subject to Lambert's law) or cosine
(the flux sent by the surface element of such a source is proportional to ). Only a completely black body strictly follows Lambert's law. The unit of brightness is candela per meter squared (cd/m2). Illumination
E– a value equal to the ratio of the luminous flux incident on a surface to the area of this surface: Illuminance unit – luxury
(lx): 1 lx – illumination of a surface on 1 m2 of which a luminous flux of 1 lm falls (1 lm = 1 lx/m2). Work order Task 1. Determining the laser light intensity. By measuring the diameter of the diverging laser beam in two of its sections, separated by a distance, we can find the small beam divergence angle and the solid angle in which the radiation propagates (Fig. 3.2): Luminous intensity in candelas is determined by the formula: Where Experiment 1. Install module 2 on the optical bench and adjust the installation according to the method described on page . After making sure that the installation is adjusted, remove module 2. 2. Place the lens attachment on the emitter (object 42). Install the condenser lens (module 5) at the end of the bench with the screen facing the emitter. Fix the coordinate of the risks of its raters. Using the condenser screen, determine the diameter of the laser beam. 3. Move the condenser to the laser 50 - 100 mm. Fix the coordinate of the mark and, accordingly, determine the beam diameter using the condenser screen. 4. Calculate the linear angle of beam divergence using formula (3.13), taking . Calculate the solid angle of beam divergence using formula (3.14) and the luminous intensity using formula (3.15). Make a standard error estimate. 5. Carry out the experiment 4 more times with other positions of the condenser. 6. Enter the measurement results into tables: Task 2. Intensity in a spherical wave The laser radiation beam is transformed by a collecting lens into a spherical wave, first converging to the focus, and after the focus - diverging. It is required to trace the nature of the change in intensity with the coordinate - . The voltmeter readings are used as values without conversion to absolute values. Experiment 1. Remove the diffuser lens attachment from the emitter. At the end of the free bench, install a microprojector (module 2) and, close in front of it, a condenser lens (module 5). Make sure that when moving module 5 away from module 2, the size of the spot on the installation screen and the radiation intensity in the center of the spot changes. Return the condenser to its original position. 2. Place a photosensor - object 38 - in the object plane of the microprojector, connect the photosensor to the multimeter, set the multimeter to constant voltage measurement mode (measurement range - up to 1 V) and remove the dependence of the voltage on the voltmeter on the coordinate of module 5 with a step of 10 mm, taking as a point reference coordinate of the risks of module 2. Make 20 measurements. 4. Give definitions of the main photometric quantities (energy and light) indicating units of measurement. 5. What is the basic unit of light in SI? How is it determined? 6. How are radiation flux and luminous flux related? 7. Which light source is called isotropic? How are luminous intensity and luminous flux of an isotropic source related? Why? 8. When is a light source called Lambertian? Give an example of a strictly Lambertian source. 9. How does the intensity of a light wave emitted by an isotropic point source depend on the distance to the source? Why? Laboratory work No. 4 To quantify radiation, a fairly wide range of quantities is used, which can be conditionally divided into two systems of units: energy and light. In this case, energy quantities characterize radiation related to the entire optical region of the spectrum, and lighting quantities characterize visible radiation. Energy quantities are proportional to the corresponding lighting quantities. The value of Fe is expressed in watts (W). – energy unit In most cases, the quantum nature of the generation of radiation is not taken into account and it is considered continuous. A qualitative characteristic of radiation is the distribution of the radiation flux over the spectrum. For radiation having a continuous spectrum, the concept is introduced spectral radiation flux density (j l)– the ratio of the radiation power falling on a certain narrow section of the spectrum to the width of this section (Fig. 2.2). For a narrow spectral range dl the radiation flux is equal to dФ l. The ordinate axis shows the spectral densities of radiation flux j l = dФ l / dl, therefore, the flow is represented by the area of an elementary section of the graph, i.e. Under luminous flux F, in general, understand the radiation power assessed by its effect on the human eye. The unit of measurement for luminous flux is lumen (lm). – lighting unit The action of the light flux on the eye causes it to react in a certain way. Depending on the level of action of the light flux, one or another type of light-sensitive receptors of the eye, called rods or cones, works. In low light conditions (for example, under the light of the moon), the eye sees surrounding objects using rods. At high light levels, the daytime vision apparatus, for which the cones are responsible, begins to work. In addition, cones, based on their light-sensitive substance, are divided into three groups with different sensitivity in different regions of the spectrum. Therefore, unlike rods, they react not only to the light flux, but also to its spectral composition. In this regard, it can be said that light effect is two-dimensional. The quantitative characteristic of the eye reaction associated with the level of illumination is called lightness. The qualitative characteristic associated with different levels of reaction of the three groups of cones is called chromaticity. Luminous intensity (I). In lighting engineering, this value is taken as main. This choice has no basis in principle, but is made for reasons of convenience, since The intensity of light does not depend on distance. The concept of luminous intensity applies only to point sources, i.e. to sources whose dimensions are small compared to the distance from them to the illuminated surface. The luminous intensity of a point source in a certain direction is per unit solid angle W light flow F, emitted by this source in a given direction: I = Ф / Ω Energy Luminous intensity is expressed in watts per steradian ( Tue/Wed). Behind lighting engineering unit of luminous intensity adopted candela(cd) is the luminous intensity of a point source that emits a luminous flux of 1 lm, distributed uniformly within a solid angle of 1 steradian (sr). A solid angle is a part of space bounded by a conical surface and a closed curved contour that does not pass through the vertex of the angle (Fig. 2.3). When a conical surface is compressed, the dimensions of the spherical area o become infinitesimal. The solid angle in this case also becomes infinitesimal: Figure 2.3 – Towards the definition of the concept “solid angle” Illumination (E). Under energetic illumination E uh understand the radiation flux on unit of area illuminated surface Q:
The irradiance is expressed in W/m2. Luminous illumination E expressed by luminous flux density F on the surface illuminated by it (Fig. 2.4): The unit of luminous illumination is taken luxury, i.e. illumination of a surface receiving a luminous flux of 1 lm uniformly distributed over it over an area of 1 m2. Among other quantities used in lighting engineering, important ones are energy radiation We or light energy W,
as well as energy Ne or light N exposition. The values of We and W are determined by the expressions where are the functions of changes in radiation flux and light flux over time, respectively. We is measured in joules or W s, a W – in lm s. Under energy H e or light exposure understand the surface radiation energy density We
or light energy W respectively on the illuminated surface. That is light exposure H this is the product of illumination E, created by a radiation source, for a time t effects of this radiation.
1. Radiation flux. The concept of the spectrum of electromagnetic radiation. The principle of measuring flux distribution over the spectrum. Energy quantities.
Spectrum of electromagnetic radiation, microns
Features of the eye as a receiver.
К= F555/Ф555=1/0.00146=680 (lm/W)
where Ф(λ) is the distribution of radiation power across the spectrum, V(λ) is the relative spectral luminous efficiency curve (visibility curve), and 680 is the coefficient that allows you to move from watts to lumens. It is called the luminous equivalent of the radiation flux and is expressed in lm/W.
A = ∫ Ф (λ) S (λ) dλ
The unit of measurement A depends on the unit of measurement of spectral sensitivity. If Sλ is a relative quantity, A is measured in watts. If Sλ has dimension, for example
uh
Where F is the radiant flux, Sλ is the sensitivity of the photodetector, Qλ is its area
6. Light source. Their spectral characteristics. Classification of light sources by type of radiation. Formula of Planck and Wien.
7. Photometric properties of radiation sources. Classification by geometric quantities: point and extended light sources, photometric body.
. (3.6)
, (3.7)
. (3.8)
, lm, (3.9)
- constant, is a function of visibility, determined by the sensitivity of the human eye to radiation of different wavelengths. The maximum value is reached at 
. The complex uses laser radiation with a wavelength 
. In this case .
. (3.10)
. (3.11)
.
(3.12)
Rice. 3.2.
, (3.13)
, (3.15)
- constant, the radiation power is set to a minimum - equal (the laser current adjustment knob is turned to the extreme counterclockwise position), - visibility function, determined by the sensitivity of the human eye to radiation of different wavelengths. The maximum value is reached at . The complex uses laser radiation with a wavelength . In this case . №
,
,
№
, %
The main quantity in the energy system that allows us to judge the amount of radiation is Fe radiation flux, or radiation power, i.e. amount of energy W, emitted, transferred or absorbed per unit time:
If the radiation spectrum lies within the range l 1 before l 2, then the magnitude of the radiation flux 
